That depends on your point of view. The relation noise to signal at pixel level is the same in FX and DX.

..which in practice means nothing.

I'm talking about actually reproducing and using the files.

If you only use half of the sensor or half of the image, then you have to enlarge your image twice as much, just as you would do with different film formats.

So beyond any question, the high ISO performance is always going to be better when you use all of the sensor rather than just half of it. "Pixel level" is meaningless in practice.

In answer to the OP, we don't actually know about the D5200 yet. Sorry.

All you said is very correct, but in the question is mentioned only "DX lens", not also the DX format. You can use a DX lens on FX format if you want, with more or less vignetting, depending on the type of lens. This will require more or less later crop.